群逆阵的一些广义逆的特征及应用  

Characterizations and Applications for Some GeneralizedInverses of Group Inverses Matrices

作　　者：路紫薇 左可正 蒋万林 LU Ziwei;ZUO Kezheng;JIANG Wanlin(School of Mathematics and Statistic,Hubei Normal University,Huangshi Hubei 435002)

机构地区：[1]湖北师范大学数学与统计学院,湖北黄石435002

出　　处：《湖北理工学院学报》2020年第4期56-62,共7页Journal of Hubei Polytechnic University

基　　金：国家自然科学基金项目(项目编号:11961076)。

摘　　要：研究了EP阵、k-广义投影算子和k-超广义投影算子的特征和性质.利用矩阵的核-幂零分解、酉-上三角分解及一些广义逆的性质,得出了群逆阵的Moore-Penrose逆、core-逆、core-EP逆的表达式.通过这些表达式给出了EP阵、k-广义投影算子和k-超广义投影算子的一些新刻画,并给出了相应的应用.The properties of EP matrices,k-generalized projectors and k-hypergenera lized projectors are studied. The expressions of the Moore-Penrose inverse, the core-inverse and the core-EP inverse of a group inverse matrix are obtained by using the core-EP decomposition, unitary-upper triangular decomposition and some properties of generalized inverses.By these expressions, some new characterizations of EP matrices, k-generalized projectors and k-hypergeneralized projectors are given, and the corresponding applications are obtained.

关 键 词：广义逆 核-幂零分解 酉-上三角分解 k-广义投影算子 k-超广义投影算子 

分 类 号：O151.2[理学—数学]